# Properties

 Label 6038.2 Level 6038 Weight 2 Dimension 379764 Nonzero newspaces 4 Sturm bound 4.55718e+06

## Defining parameters

 Level: $$N$$ = $$6038 = 2 \cdot 3019$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$4$$ Sturm bound: $$4557180$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6038))$$.

Total New Old
Modular forms 1142313 379764 762549
Cusp forms 1136278 379764 756514
Eisenstein series 6035 0 6035

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6038))$$

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
6038.2.a $$\chi_{6038}(1, \cdot)$$ 6038.2.a.a 2 1
6038.2.a.b 54
6038.2.a.c 57
6038.2.a.d 69
6038.2.a.e 70
6038.2.c $$\chi_{6038}(239, \cdot)$$ n/a 502 2
6038.2.e $$\chi_{6038}(9, \cdot)$$ n/a 127006 502
6038.2.g $$\chi_{6038}(5, \cdot)$$ n/a 252004 1004

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6038))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6038)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(3019))$$$$^{\oplus 2}$$